In order to be able to adapt aircraft flexibly to different passenger or cargo requirements, whether by refurbishing or retrofitting, fastening devices are for example known from U.S. Pat. No. 6,902,365 B1 and U.S. Pat. No. 7,021,596 B2. The devices are developed from standardised fastening structures such as are provided in the floors of aircraft cabins. Fastening devices are proposed which comprise co-operating clamping jaws in order to securely fix the respective fixture, such as for example a passenger seat or container, to the fastening structure.